Why is Work Negative in PV diagram?

[lc99]

Homework Statement

Homework Equations

The Attempt at a Solution

Was wonder how the isotherm is negative? Is it because it is going counterclockwise (the arrows)? If this is the case, i don't see why a-c would be positive work...

I'm just confused on whether work should be positive or negative... :(

 

[haruspex]

Was wonder how the isotherm is negative? Is it because it is going counterclockwise (the arrows)? If this is the case, i don't see why a-c would be positive work...

It is not to do with the direction around the loop but rather the direction along the V axis. Work is ∫P.dV. If it is going leftward along the V axis then dV is negative.
This is taken care of by the integrals if you are careful with the limits.

 

[Dr Dr news]

From a→c, you are taking work out, from c→b, you are putting work in and since you are putting more work in that you are taking out, the net work is negative. You might think of it as one process at a time, the area under a→c represents the work out and the area under c→b represents the work in, the net work/cycle is the area enclosed on the p-V diagram. Of course if you reverse the direction around the enclosed area, the net work is positive.